Iterative hard thresholding for compressed data separation

We study the problem of reconstructing signals' distinct subcomponents, which are approximately sparse in morphologically different dictionaries, from a small number of linear measurements. We propose an iterative hard thresholding algorithm adapted to dictionaries. We show that under the usual assumptions that the measurement system satisfies a restricted isometry property (adapted to a composed dictionary) condition and the dictionaries satisfy a mutual coherence condition, the algorithm can approximately reconstruct the distinct subcomponents after a fixed number of iterations. (C) 2020 Elsevier Inc. All rights reserved.